Question

Find the zeros of the polynomial f(x) = x3 -5x2 -16x + 80, if its two zeros are equal in
magnitude but opposite in sign.

Answer 1

Answer:

α=-4, β=4, r=5

Step-by-step explanation:

x³-5x²-16x+80=0

⇒a=1, b=-5, c=-16, d=80

given:α=-β

⇒α+β=0...  (i)

α+β+r=-b/a

from (i)

⇒r=-(-5)=5....   (ii)

αβ+βr+rα=c/a

αβ+r(α+β)=-16

-β²+r(0)=-16

-β²=-16

β²=16

β=4

⇒α=-4

so α=-4, β=4, r=5

hope this helps